How large a sample is needed to estimate the regional variogram adequately?

Summary

There is little to guide the geostatistical practitioner on the size of sample needed to estimate the variogram adequately. It is often estimated from few data, but because confidence limits cannot be determined analytically from a single set of data its precision is unknown. Approximate confidence intervals can be found numerically by Monte Carlo simulation. A large field of values is created using a plausible model of the variogram. It is then sampled many times, and the observed variogram of each sample is computed. An experimental sampling distribution of the variogram is constructed from which percentiles and confidence limits can be obtained. Our experiments suggest that variograms computed on fewer than 50 data are of little worth and that at least 100 data are needed. For a normally distributed isotropic variable 150 data should suffice, while one derived from 225 data will usually be reliable.